Computing Robust Forward Invariant Sets of Multidimensional Nonlinear Systems via Geometric Deformation of Polytopes

• 成果类型: Article
• 署名作者: Ameen, Taha; Mukhopadhyay, Shayok; Qaddoumi, Nasser
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University New Haven; American University of Sharjah
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3300349
• 发表日期: 2023
• 页码: 8293-8300
• 关键词: Computational topology; invariant sets; nonlinear dynamical systems; robust forward invariance

摘要

This article develops an algorithm to compute the sequences of polytopic robust forward invariant sets (RFIS) that vary in size for a nonlinear dynamical system. This is done through a novel approach that geometrically deforms a polytope into an invariant set using a sequence of homeomorphisms, based on an invariance condition that only needs to be satisfied at a finite set of test points. A fast computational test is also developed to check if a given polytopic set is an RFIS. Our approach is applicable to arbitrary Lipschitz continuous nonlinear systems in the presence of bounded additive disturbances, and its versatility is presented through simulation results on a variety of nonlinear dynamical systems in two and three dimensions.